SOLUTION: Problem Solving: A sunflower plant was purchased with the following growth guarantee. After being planted, on the first day it would grow 100 mm. On the second day its height would

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Question 466249: Problem Solving: A sunflower plant was purchased with the following growth guarantee. After being planted, on the first day it would grow 100 mm. On the second day its height would increase by one half (50%), on the third day by one third, on the fourth day by one fourth, and so on. Assuming that the plant actually grows according to the guarantee, how many days would it take for it to reach its maximum height of 5000 mm?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A sunflower plant was purchased with the following growth guarantee.
After being planted, on the first day it would grow 100 mm.
On the second day its height would increase by one half (50%),
on the third day by one third, on the fourth day by one fourth, and so on
Assuming that the plant actually grows according to the guarantee, how many days would it take for it to reach its maximum height of 5000 mm?
:
Day 1: 100
Day 2: 100 + 1%2F2*100 = 150
Day 3: 150 + 1%2F3*150 = 200
Day 4: 200 + 1%2F4*200 = 250
Day 5: 250 + 1%2F5*250 = 300
Day 6: 300 + 1%2F6*300 = 350
Day 7: 350 + 1%2F7*350 = 400
From this we can see a pattern, that every day it will increase by 50:
50(d+1) = 5000
50d + 50 = 5000
50d = 5000 - 50
50d = 4950
d = 4950%2F50
d = 99 days to reach 5000 mm